Real Algebraic and Analytic Geometry

213. Tobias Kaiser, Jean-Philippe Rolin, Patrick Speissegger:
Transition maps at non-resonant hyperbolic singularities are o-minimal.

e-mail: , ,

Submission: 2006, December 23.

Abstract:
We construct a model complete and o-minimal expansion of the field of real numbers such that, for any planar analytic vector field X and any isolated, non-resonant hyperbolic singularity p of X, a transition map for X at p is definable in this structure. This structure also defines all convergent generalized power series with natural support and is polynomially bounded.

Mathematics Subject Classification (1991): 37C27, 37E35, 03C64.

Keywords and Phrases: Dynamical Systems; Logic.

Full text: http://arxiv.org/abs/math.DS/0612745

Server Home Page